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Department of Mathematics

Karlsruhe Institute of Technology
D-76128 Karlsruhe
Germany
Tel.: +49 721 608-43800

Asymptotische Methoden der angewandten Mathematik (Summer Semester 2012)

Lecturer: Tomas Dohnal
Classes: Lecture (0155000), Problem class (0155100)
Weekly hours: 2+1


Only rarely can one solve differential equations explicitly using elementary functions. However, wenn local information on the solution is sufficient (local, e.g., in the value of a parameter or in the time or space variable), then there are powerful asymptotic methods for the approximation of the solution.

We are going to discuss basic asymptotic methods for the aproximation of integrals and solutions of differential equations.

Schedule
Lecture: Monday 9:45-11:15 1C-04
Problem class: Friday 9:45-11:15 (every 2nd week) 1C-03 (Start 27.4.)
Lecturers
Lecturer, Problem classes Tomas Dohnal
Office hours: Di: 9:30-11:00 (oder nach Vereinbarung)
Room 211 IWRMM (20.52)
Email: dohnal@kit.edu

- 'little o' and 'big O' notation
- asymptotic sequences and series
- approximation of integrals: Watson's lemma, method of steepest descent
- series expansion for linear differential equations
- perturbation theory: regular and singular perturbations
- method of matched asymptotics
- multiple scales analysis

References

H.J.J. Roessel and J.C. Bowman, Asymptotic Methods, lecture notes, University of Alberta, Edmonton, Canada, 2012.
http://www.math.ualberta.ca/~bowman/m538/m538.pdf

C. Bender and S. Orszag, Advanced Mathematical Methods for Scientists and Engineers, Springer, 1999.